Balancing transformations for unstable nonminimal linear systems

It is shown that an unstable nonminimal continuous (discrete) realization (A, B, C) can be transformed via a similarity transformation into a balanced one if and only if the product of the controllability, observability Gramians is similar to a real diagonal matrix Lambda . If, in addition, the eigenvalues of A, say lambda , satisfy the relation lambda /sub i/+ lambda /sub j/ not=0( lambda /sub i/ lambda /sub j/ not=1) then the matrix Lambda will always be positive semidefinite, and a balanced realization with its minimal part in the internally balanced form can always be obtained.>